Differentiating the Area of a Circle

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  • #1
S.R
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In my high school Calculus course, I've encountered several optimization problems involving the area of a circle and I noticed the obvious fact that if you differentiate the area of a circle you obtain the expression for its circumference. This implies that the rate of change of a circle's area is equal to its circumference (which is difficult to visualize). So what does notion actually mean?

S.R
 

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  • #2
tiny-tim
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Hi S.R! :smile:

It means that the whole area is made of lots of little circumferences …

if you subtract one area from a slightly larger one, you get a circumference. :wink:

(works for spheres also!)
 
  • #3
S.R
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Oh :D Essentially the area consists of concentric circles?
 
  • #4
tiny-tim
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yup! :biggrin:
 

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